Isometries of R2 and R3 - Specific example

On page 462, Papantonopoulou defines translations, rotations and reflections for R2 and R3 (see attached). Note that the rotations are defined as about the origin and the reflections are about the X-axis or axis.

Then on Page 463 he states Theorem 14.21 as follows:

14.21 Theorem An isometry S of or can be uniquely expressed as where i = 0 or 1

I would like to use Theorem 14.21 to specify S for the isometry of that maps the line y = x to the line y = 1 - 2x? [ ie what is , , in this case?]